THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 283 



continues decreasing, everything occurring as witli .the frame of Fig. 30 ; but 

 the pentagonal film decreases much more r.ipidly, then disappears, and at the 

 instant the system undergoes an abrupt change, assuming an odd arrang<-ment 

 ■which it would be difficult to represent clearly in perspective, but of which I 

 shall still attempt to give an idea. On the two bases respectively rest two iden- 

 tical assemblages, composed of five curved • films ; one of these assemblages is 

 Fi"- 3S represented in projection on the plane of the base by Fig. 38 

 It will be seen that there are in each of them a pentagonal film, 

 two quadrangular and two triangular films. These two assem- 

 blages are connected with each other by films which [)roceed 

 from the five lateral edges of the prism, and by two other inter- 

 mediate films, whose direction is also in the length of the frame, 

 and which proceed from the liquid edges a h and h c of one of these assem- 

 blages to terminate at the homologous liquid edges of the other. There is no 

 need of remarking that the same thing would occur if, instead of overpassing 

 the indicated limit, we should simply attain it — that is to say, if we gave to 

 the prism the height which Avould precisely correspond to the annulling of 

 the pentagonal film ; in eftect there would then be ten liquid edges terminating 

 at the centre of the system, iu the same liquid point, and consequently equili- 

 brium would be unstable. 



§ 31. Although, in the laminar systems of the prisms with a greater number 

 of sides, the oblique films must be considerably curved, it appeared to me pro- 

 bable that there would also be, lor each of these prisms, a limit of height beyond 

 which the system would no longer comprise a central polygonal film, and that 

 this limit would differ little from that pertaining to the pentagonal prism. To 

 ascertain this, I tried first the hexagonal prism, with a frame whose height was 

 also about 2h times the diameter of the circle which might be inscribed at the 

 base. Now, to my great surprise, a central hexagonal film was still formed, 

 though much smaller than with the frame of § 20 ; but the system had under- 

 gone a modification which rendered possible the existence of this film. The 

 poiuts of the solid lateral edges from which proceeded the oblique liquid edges 

 (§ 26) were situated much further from the summits of the bases, so that the ar- 

 rangement was very nearly such as if, in reality, the frame had been shortened. 

 In this arrangement, therefore, the films proceeding from the sides of the two 

 bases remain, to a sufficently great distance from the latter, adherent to the solid 

 lateral edges, whence it follows that the assemblage should be considered as an 

 imperfect laminar system, resulting from a conflict between the tendency of the 

 films to occupy the lateral faces of the prism, and the kind of traction which 

 these films undergo on the part of the hexagonal film which ascends among 

 them. I say imperfect, because the films which proceed from all the sides of 

 the same base are, iu the parts which remain attached to the lateral solid edges, 

 separated from one another and rendered independent by these edges. 



§ 32. This becomes more evident Avith prisms the number of whose lateral 

 faces exceeds six ; then the angle of two adjacent lateral faces being superior to 

 120^, the films have more tendency to occupy all these faces, and the portions 

 which remain attached to the lateral solid edges are, in effect, much more ex- 

 tended. For example, witii an octagonal frame iu which the ratio between the 

 height and the diameter of the circle inscribed at the base is nearly the same as 

 in the above frames, the central octagonal film, instead of being small, is, on the 

 contrary, very great, and the two oblique liquid edges proceeding from any one of its 

 summits attach themselves to the corresponding solid lateral edge, at two points, 

 of which the distance is but about the sixth of the length of that edge, and con- 

 sequently a little less than the half of the diameter of the circle inscribed at the 

 base. In this case, therefore, the films which proceed from two homologous 

 sides of the bases in order to direct themselves towards the central octagonal 

 film, only abandon the solid lateral edges on approaching the middle of the 



